Whether something is conscious is important for many reasons, not least the ethical implications. You and I have internal lives, and we expect others to respect that somewhat, because ignoring it is hypocrisy (if you ignore my wishes, should anybody care about yours?) and cruelty (ignoring my wishes causes me to suffer).
Something doesn't need to be empirically verifiable, let alone scientifically, to be true. Neither of us can prove that we have internal lives, but neither of us questions it -- and we consider it important enough that most of us think it entitles us to certain rights.
Absolutely none of this is amorphous. It's precise and unambiguous, and has enormous implications. History also shows everywhere that we're better, kinder, and more responsible when we choose to care about it.
Whether LLMs are conscious matters in more practical ways, too, because beliefs about these things alter the way people use and think about them. If I think an LLM is conscious, then I think it's capable of something like knowledge or values. Human beings, moreover, are social creatures. These tools are dangerous and seductive precisely because they tap into that part of us. Denying LLMs are conscious and rejecting the parts of them that take advantage of our social-animal wetware is intellectual self-defense. I'm not sure how effective it is (it doesn't stop us from responding to the convincing social cues that the tools feed us), but I have to think it's better than nothing, and it's certainly less dangerous than the belief that the tools are conscious.